Clean it up!

• In Lab 1F, we saw how we could clean data to make it easier to use and analyze.
  • You cleaned a small set of variables from the American Time Use (ATU) survey.
  • The process of cleaning and then analyzing data is very common in Data Science.
• In this lab, we’ll learn how we can create frequency tables to detect relationships between categorical variables.
  • For the sake of consistency, rather than using the data that you cleaned, you will use the pre-loaded ATU data.
  • Use the data() function to load the atu_clean data file to use in this lab.

How do we summarize categorical variables?

• When we’re dealing with categorical variables, we can’t just calculate an average to describe a typical value.
  • (Honestly, what’s the average of categories orange, apple and banana, for instance?)
• When trying to describe categorical variables with numbers, we calculate frequency tables

Frequency tables?

• When it comes to categories, about all you can do is count or tally how often each category comes up in the data.
• Fill in the blanks below to answer the following: How many more females than males are there in our ATU data?

tally(~ ____, data = ____)

2-way Frequency Tables

• Counting the categories of a single variable is nice, but often times we want to make comparisons.
• For example, what if we wanted to answer the question:
  • Does one gender seem to have a higher occurrence of physical challenges than the other? If so, which one and explain your reasoning?
• We could use the following plot to try and answer this question:

bargraph(~phys_challenge | gender, data = atu_clean)

• The split bargraph helps us get an idea of the answer to the question, but we need to provide precise values.
• Use a line of code, that’s similar to how we facet plots, to obtain a tally of the number of people with physical challenges and their genders.

Interpreting 2-way frequency tables

• Recall that there were 1153 more women than men in our data set.
  • If there are more women, then we might expect women to have more physical challenges (compared to men).
• Instead of using counts we use percentages.
• Include: format = "percent" as an option to the code you used to make your 2-way frequency table. Then answer this question again:
  • Does one gender seem to have a higher occurrence of physical challenges than the other? If so, which one and explain your reasoning?
  • Did your answer change from before? Why?
• It’s often helpful to display totals in our 2-way frequency tables.
  • To include them, include margins = TRUE as an option in the tally function.

Conditional Relative Frequencies

• There is as difference between phys_challenge | gender and gender | phys_challenge.

tally(~phys_challenge | gender, data = atu_clean, margin = TRUE)

##                 gender
## phys_challenge   Male Female
##   No difficulty  4140   5048
##   Has difficulty  530    775
##   Total          4670   5823

tally(~gender | phys_challenge, data = atu_clean, margin = TRUE)

##         phys_challenge
## gender   No difficulty Has difficulty
##   Male            4140            530
##   Female          5048            775
##   Total           9188           1305

• At first glance, the two-way frequency tables might look similar (especially when the margin option is excluded). Notice, however, that the totals are different.

• The totals are telling us that R calculates conditional frequencies by column!

• What does this mean?

  • In the first two-way frequency table the groups being compared are Male and Female on the distribution of physical challenges.
  • In the second two-way frequency table the groups being compared are the people with No difficulty and those that Has difficulty on the distribution of gender.

• Add the option format = "percent" to the first tally function. How were the percents calculated? Interpret what they mean.

On your own

• Describe what happens if you create a 2-way frequency table with a numerical variable and a categorical variable.
• How are the types of statistical questions that 2-way frequency tables can answer different than 1-way frequency tables?
• Which gender has a higher rate of part time employment?